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All together you have improved a lot, Weiyan, and I hope you can hear those two slow 3rds (compare them and, if you wish, let me know) and G#4.

You wrote: ..."The octave may be little bit wider."...

Yes, you were right and you seem you are able to perceive also "fine" issues.

..."Tune the 12th pure. The mistake in temperament is reflected in octave when a note cannot tune pure 12th."...

Correct, like 10ths, 15ths and 17ths... 12ths work as a good "meter" and as a confortable reference for the Pre-form tuning. Keep on thinking in terms of "whole" geometry and interweaving all intervals and... enjoy your tunings.

Retuned the piano with Verituner ET, so can't check the G#4. I tuned the whole piano with Verituner to compare the sounding of ET with CHAS. For chords in higher octaves, CHAS seems rather calm. THis may due to inverted fifth progression.

The base: All these five intervals (below) sound too pure (too still/no movement/no beat). In particular:

A3-A4: Very "just" (you want A4 on the wide side)A3-E4: Too close to just E4-A4: As aboveA3-D4: As above (you want D4 wide, very close to 1 bps)D4-A4: As above

Now, if we were to think in terms of "one-single-key and few intervals" (within one-single-octave) we may perhaps accept those "just" intervals, but really we want all keys and all intervals (no matter which octave) to sound in tune. As a consequence of "just" intervals we would get other intervals that are sensibly far from just, so missing the harmoniousness of the whole.

And you would remember that A3 and E4 and D#4 need to go down a bit (in pitch).

From your second last post:

..."The D4-G4 seems very stretch.D#4-G4 not sure too fast or too slow.Its rather difficult to hear bit in 4th octave.

Is it possible to use F3-F4 octave?"...

To me, D4-G4 sounds inverted (G4 should go up), and D#4-G4 is too slow. In general, make sure that the five Base-intervals are on the right side. And yes, do experiment other sequences (perhaps of your own too) and the F3-F4 compass, in which case I'd get to F3 as fast as possible, so to avoid piling up approximations.

You wrote: ..."Its far from OK as I heard. I am begin to recognize thirds."...

You are right, it's not Ok but... it is important that you can realize that yourself. You may listen again to these last recordings and notice some "very different" intervals, related to three notes: C4, D#4 and G4. Try to compare intervals, and try to focus on large, very evident differences caused by those notes. And the M3rd D#4-G4 is not so bad only because both notes are very high (in pitch). Also E4 has gone down too much, in fact A3-E4 is too narrow (about 2 bps). Do not worry if sometime you do not get a satisfactory result, this is how we learn and... sometime we regress as well.

We can use M6ths like M3rds, comparing chromatic intervals and (their relative) beat-progressions; I also evaluate - aurally - their "taste", their "tension", whether it sounds "salty" (listen again to B3-D#4) or too "loose" (C4-E4). Start developing an idea of what 6ths can sound like, you can start from A3-F#4... then you will be able to compare A#3-G4, B3-G#4 and C4-A4.

..."I only use tenths to tune bass notes."...

Personally, I use 10ths also going up the scale, the first 10th being A3-C#5: that helps me evaluate the octaves (A#3-A#4 etc...) progressive stretch; A3-C#5 tells me the kind of curve I'm drawing while stretching octaves, until I get to the first 12th, A3-E5. From E5 up (and in general), 12ths are very "imperative" and yet easy to "evaluate". Going down the bass I use octaves, 4ths and 5ths and check with 10ths, 12ths, 15ths and 17ths.

..."Should I tune the 12ths pure?"...

Good question. Is "tuning" the tuning of... one interval? Hmmm... I do not think so. But if you find yourself far away from a pure 12th you may still improve your tuning. Chas 12ths beat (narrow) at a constant and very very slow beat-rate, but we may have good reasons for tuning pure or even wide 12ths, depending on the single piano's condition. Would you not regret having tuned "pure 12ths" if, at the end of your tuning, some 12ths were to sound flat?

Sixths is are helpful. Compared the progressiveness of sixths help to sort out some mistake.

Tune the whole piano, its un-playable. Tune again from temperament.

This time tune bass first. On top of octave, use 5ths, 10ths, 15ths and 17ths and compound fifths. The mistake in temperament is revealed. Some intervals in wrong side is revealed in this process. Play some chord, its full of bass. Not treble is not tuned yet.

This Sunday morning I played some chords, find the F chord offensive. Further deep into it, find A3-C4 offensive. Compared with other m3s, it has different character. Finally retuned whole temperament.

Very good job, you have sensibly improved all intervals. I'm glad you can also use m3rds and M6ths, as well as larger intervals... as you say they reveal any approximation and help perfecting both the "temperament" and the overall tuning-form.

Let's try to further refine your last tuning, by listening again to some intervals that can be improved.

The base:

A3-A4: Ok, now we hear some "movement"A3-E4: Ok... E4-A4: Ok, a little too wide... A3-D4: Ok, it can be wider, closer to 1 bpsD4-A4: Ok...careful, it may be inverted

(*): While I'm tuning the base, I consider "normal" having to correct A3, E4 and D4. In the case above, A3 can go down a bit (with a Forte blow), so improving your base.

Fine corrections:

A3-A4: Good (*), a little bit shy, it can be a little bit widerA3-E4: Ok (*), if A3 goes (a little bit) down, E4 can also go down a bitE4-A4: Ok, you want this 4th a little fasterA3-D4: Ok (*), make it closer to 1 bps, if anything... abundant, you may adjust it later with a ForteD4-A4: Ok

This is good, as we are getting into fine "hair" corrections, good for truly progressive beating and singing unisons.

…"Readjusted yesterday's tuning."…

Very good job indeed.

…"Used about three hours to tune F3-B4."…

Is that right, F3-B4 in about three hours? Hmmm… that would be far too long. Let me know if you can sing the note you tune… we might be able to sort out a faster procedure.

…"I think in coming days will focus on octaves."…

That's good. Let me know if you want to spend some time on your last recordings (6 Sept.).

…"Still not know how to use double octave + 7ths."…

That's quite straightforward: play (for example) C2-A#4, it beats very very fast… so fast that we cannot distinguish beats… go - chromatically - down the bass (slowly) until you can actually hear/distinguish beats (expect fast beating) and use them to order their progression. Slow-bps = bottom note is high in pitch; Fast-bps = bottom note is low. As mentioned, do not trust one single interval, use all intervals and beats that can help you to manage and "position" the bass pitch, use fifths, octaves, 10ths, 12ths, 15ths, 17ths and, not last, use your sense of "in tune".

Practicing left hand is for spreading the work load of right hand. For higher register, its easier for left hand in seating position. For base notes I use right hand. This is ergonomic. Base string leaned leftward. Play with left and tune with right hand have better posture. For treble note is just opposite. I also found use left hand, the hammer in ten o'clock is easier to raise pitch little by little.

The slow speed is due to low proficiency level. Take time to check interval directions. Evaluate tuning by playing chords in all keys. Then diagnostic for inconsistent colors and correction.

Although I think practice can improve speed, still looking for faster procedure.

..."Practicing left hand is for spreading the work load of right hand. For higher register, its easier for left hand in seating position. For base notes I use right hand. This is ergonomic. Base string leaned leftward. Play with left and tune with right hand have better posture. For treble note is just opposite. I also found use left hand, the hammer in ten o'clock is easier to raise pitch little by little."...

Yes, it is similar to the base, mainly proceed with three Slow-Beating-Intervals intervals and further check (and perfect) with Fast-BI's. I use 8's, 12ths and 15ths... and check with 17ths. C7-C8... also check fifths, I like to hear them (apparently) pure.

Yes, tuning requires going through chromatic intervals, interrelating (getting the most correct (univocal/coherent) relation amongst) all intervals and their chromatic beat-curves, all across the keyboard. This (only) can really shape a sound-whole.

If possible, listen to the 10ths again, you'll notice that the 10th on A4 is much slower than the previous (F#3-A#4, this beats fast) and equal beating with the next down (E3-G#4). Now, in this sequence (going down the bass)... beats must slow down progressively. See, in the case above, we have the first 10th very fast and the following two 10ths are much slower (and equal beating). Please, let me know if you can notice that.

The other intervals:

5th, D#-A#, make it closer to just8th, as above10th, Ok... tense15th, 17th, Ok. Please note, in this range 15ths (on their own) are not much significant, as our ear is pretty "generous" here.

A3-A4: Ok...A3-E4: make it narrow-closer to justE4-A4: OkA3-D4: this beats about 2 bps, make it (wide) closer to 1 bpsD4-A4: as above, too much "movement", make it almost just (you want to invert the fifths beat rate progression)

Thirds:

A3-C#4: Too slow, about 3 bps, check C#4-F#4… very "salty" (very tense), raise C#4 A#3-D4: Ok, much faster than previous, let me know if you can hear that (we will correct your next tuning)B3-D#4: Slower than previous, around 6 bps, more typical of E3-G#3 C4-E4: Ok, a bit too tense C#4-F4: Ok, as above D4-F#4: Ok, sweeter than previous (try to "feel" this difference) D#4-G4: Ok, it gets less tense, make it go the other way around E4-G#4: As above F4-A4: Ok

Yes, it is "hands and ear (and breath/rythm)" coordination. Strangely enough, it may be more difficult when you go down in pitch. In general, make (feel) the pin rotate counter-clock and get to "just/narrow"; play a "forte" (for spreading the string's tension); now that your pitch is flat, (step one) get close to "just" only under pin torque/bending; then make the pin rotate (wide-clock-wise (*)) at its bottom (you may clearly feel that), change the hammer's position (on vertical at 12/11) and counter-charge the pin by exerting some steady/continuous force onto the hammer, towards the string and try to get to the "spot" with one more "forte".

(*) How much should the pin rotate... depends on the pin's elasticity, which you can evaluate in step one. In time, step-one will allow your brain to calculate the exact pin-rotation needed in order to get the wanted-pitch-as-the-result of pin-counter-charge.

..."Learn to trust my ear."...

You are right, and we can use two ears, one for intonation (meaning color, taste, feelings etc...) and one for beats rhythm, the latter being absolutely real and shareable.